Mixed complementarity problems don’t support equality constraints.
Did you try formulating as an MPEC?
Note that you need m = Model(Ipopt.Optimizer) instead of m = Model(solver=IpoptSolver()). I opened a PR to fix: Fix syntax in README by odow · Pull Request #65 · chkwon/Complementarity.jl · GitHub
If you’re still stuck, please provide reproducible code of what you’ve tried so far: Please read: make it easier to help you